 # Calculating Percentages

## Presentation on theme: "Calculating Percentages"— Presentation transcript:

Calculating Percentages
Int 2 Simple Interest / Compound Compound Interest Appreciation / Depreciation Inflation / Working back Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Starter Int 2 created by Mr. Monday, April 10, 2017

Calculating Percentages
Int 2 Compound Interest Appreciation More Simple Interest Just Calculating Percentages Inflation Rising Prices Depreciation Less Working backwards Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Learning Intention Success Criteria To understand the term simple interest and compound interest. To know the meaning of the term simple interest. To know the meaning of the term compound interest. 3. Know the difference between simple and compound interest. Monday, April 10, 2017 created by Mr.

Calculating Percentages
Just working out percentages Int 2 Simple Interest I have £400 in the Bank. At the end of each year I receive 7% of £400 in interest. How much interest do I receive after 3 years. How much do I now have? Monday, April 10, 2017 created by Mr.

Now try Exercise 1 Ch2 (page 8) Odd Numbers Calculating Percentages
Int 2 Now try Exercise 1 Ch2 (page 8) Odd Numbers Monday, April 10, 2017 created by Mr.

Calculating Percentages
Interest calculated on new value every year Int 2 Compound Interest Real life Interest is not a fixed quantity year after year. One year’s interest becomes part of the next year’s amount. Each year’s interest is calculated on the amount at the start of the year. Principal value Example Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the simply interest and then the compound interest after 3 years. Monday, April 10, 2017 created by Mr.

Calculating Percentages
Interest calculated on new value every year Compound Interest Int 2 Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compound interest and the amount he has in the bank after 3 years. Simple Interest Y1 : Interest = 7% of £400 = £28 Amount = £400 + £28 = £428 Interest = 7% of £400 = £28 Y 2 : Interest = 7% of £428 = £29.96 3 x 28 = £84 Amount = £428 + £29.96 = £457.96 Y 3 : Interest = 7% of £ = £32.06 Amount = £ £32.06 = £490.02 Simple Interest is only £84 Compound is £ £400 = £90.02 Monday, April 10, 2017 created by Mr.

Now try Exercise 2 Ch2 (page 8 & 9) Calculating Percentages
Int 2 Now try Exercise 2 Ch2 (page 8 & 9) Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Starter Int 2 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Learning Intention Success Criteria To understand how to use the calculator to calculate compound interest easier. To calculate compound interest using calculator.. Show appropriate working when solving problems. Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 This is called the multiplier. Using a calculator to do Compound Formula n = period of time Days, months years IMPORTANT Can only use this when percentage is fixed I = initial value ± = increase or decrease V = Value Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Using a calculator to do Compound questions Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is £400. n = 3 I =400 ± = increase =1.07 V= 400 x (1.07)3 = £490.02 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Using calculator to calculate Compound questions In a jar bacteria grows 4% every hour. Initially there were 200 bacteria in the jar. How many bacteria are in the jar 4 hours later. n = 4 I =200 ± = increase =1.04 V= 200 x (1.04)4 = 234 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Using calculator to calculate Compound questions A car reduces in price by 14% each year. Initially it cost £ much is it worth 5 years later. n = 5 I =12 500 ± = increase =0.86 V= x (0.86)5 = £ Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Now try worksheet Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Starter Int 2 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Learning Intention Success Criteria To understand the terms appreciation and depreciation. To know the terms appreciation and depreciation. Show appropriate working when solving problems containing appreciation and depreciation. Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Appreciation / Depreciation Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value Monday, April 10, 2017 created by Mr.

Average house price in Ayr has appreciated by 79% over past 10 years.
Quicker Method Easier 1.79 x 64995 = £ Average house price in Ayr has appreciated by 79% over past 10 years. If you bought the house for £64995 in 1994 how much would the house be worth now ? Appreciation = 79% x £ 64995 = 0.79 x £64995 = £ New value = Old Value + Appreciation = £ £ = £ Just working out percentages Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Calculating Percentages Int 2 A Mini Cooper cost £ in 2002 At the end 2003 it depreciated by 23% At the end 2004 it will depreciate by a further 16% What will the mini cooper worth at end 2004? End 2003 Depreciation = 23% x £14625 = 0.23 x £14625 = £ New value = Old value - Depreciation = £ £ = £ Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Calculating Percentages Int 2 End 2003 Depreciation = 23% x £14625 = 0.23 x £14625 = £ New value = Old value - Depreciation = £ £ = £ End 2004 Depreciation = 16% x £ = x £ = £ New Value = £ £ = £ Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Now try MIA Ex 4 Ch2 (page 12) Odd Numbers Monday, April 10, 2017 created by Mr.

created by Mr. lafferty @ www.mathsrevision.com
Starter Int 2 5cm 6cm Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Learning Intention Success Criteria Understand term inflation and work out associated real-life problems. Know the term inflation. Work out real-life problems involving inflation. Monday, April 10, 2017 created by Mr.

Calculating Percentages
Measure of how much prices rise each year. Int 2 Inflation Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 1 In 2004 a worker received a wage of £300 per week. If inflation is 2% in 2004, what should be his wage be in 2005. 2004 inflation = 2% 2% of £300 = £6 His wage should be £300 + £6 = £306 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Measure of how much prices rise each year. Int 2 Inflation Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 2 In 2002 a CD cost £8. The cost increases in line with inflation. What is the price in 2003 if inflation is 1.5%. 2002 inflation = 1.5% 1.5% of £8 = £0.12 Price is £8 + £0.12 = £8.12 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Now try MIA Ex 6 Ch2 (page 15) Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Reversing the change Example 1 After a 10% increase the price of a house is £ What was the price before the increase. 100 % % = £88 000 Deduce from question : 110 % = £88 000 We have : 1 % : Price before is 100% : £800 x 100 = £80 000 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Reversing the change Example 2 The value of a car depreciated by 15%. It is now valued at £2550. What was it’s original price. 100 % % = £2 550 Deduce from question : 85 % = £2 550 We have : 1 % : Price before is 100% : £30 x 100 = £3 000 Monday, April 10, 2017 created by Mr.

Calculating Percentages
Int 2 Now try MIA Ex 7 Ch2 (page 17) Monday, April 10, 2017 created by Mr.